Problem: $ {-3\cdot \left[ \begin{array}{cc} 4 & 2 \\ -2 & 1 \\ 3 & 1 \end{array} \right]=}$
Answer: The Strategy To multiply a matrix by a scalar, we multiply each term of the matrix by the scalar. Multiplying each term $ {\begin{aligned}-3\cdot \left[\begin{array}{rr} {4} & {2} \\ {-2} & {1} \\ {3} & {1} \end{array}\right]&=\left[\begin{array}{rr} -3\cdot{4} & -3\cdot{2} \\ -3\cdot{-2} & -3\cdot{1} \\ -3\cdot{3} & -3\cdot{1} \end{array}\right] \\\\&=\left[\begin{array}{rr} {-12} & {-6} \\ {6} & {-3} \\ {-9} & {-3} \end{array}\right]\end{aligned}}$ Summary $ {-3\cdot \left[ \begin{array}{cc} 4 & 2 \\ -2 & 1 \\ 3 & 1 \end{array} \right]=\left[ \begin{array}{cc} -12 & -6 \\ 6 & -3 \\ -9 & -3 \end{array} \right]}$